The value of log 8 base 2 is equal to 3, that is, log_{2}8 =3. In this post, we will find the value of the logarithm of 8 when the base is 2.

We will now find the value of log 8 when the base is 2.

## How to Find log_{2}8

**Question: What is log8 base 2?**

Answer: The value of log_{2}8 is 3. |

**Solution:**

**Step 1:**

At first, we will factorize the number 8. Observe that 8 is an even number, so it is divisible by 2, and we can have

8 ÷ ${\color{red} 2}$ = 4

Again, 4 is an even number, so we have

4 ÷ ${\color{red} 2}$ = 2

Similarly,

2 ÷ ${\color{red} 2}$ = 1

Once, we get 1 we will stop and the number 8 can be written as the product of red-colored numbers. That is,

8 = 2×2×2

⇒ 8 = 2^{3}

**Step 2:**

Now, taking the logarithm with base 2 on both sides, we get that

log_{2}8 = log_{2}2^{3}

⇒ log_{2}8 = 3 using the logarithm rule log_{b}b^{m} = m.

**Therefore the value of log 8 with base 2 is 3.**

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## FAQs

### Q1: What is the value of log 8 when base is 2?

Answer: As 8=2^{3}, the logarithm of 8 with base 2 is equal to 3.